{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T14:22:53Z","timestamp":1783088573721,"version":"3.54.6"},"reference-count":22,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica &quot;Francesco Severi&quot;","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100017142","name":"Gruppo Nazionale per il Calcolo Scientifico","doi-asserted-by":"publisher","award":["PRIN 2022XZSAFN"],"award-info":[{"award-number":["PRIN 2022XZSAFN"]}],"id":[{"id":"10.13039\/100017142","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.jcp.2026.115061","type":"journal-article","created":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T14:58:24Z","timestamp":1779807504000},"page":"115061","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["On the construction of nested explicit Runge\u2013Kutta methods via null rules"],"prefix":"10.1016","volume":"563","author":[{"given":"M.R.","family":"Belardo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F.","family":"Calabr\u00f2","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G.","family":"Izzo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Messina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Veneroso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"7","key":"10.1016\/j.jcp.2026.115061_bib0001","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1134\/S0965542520070076","article-title":"Nested implicit Runge\u2013Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations","volume":"60","author":"Kulikov","year":"2020","journal-title":"Comput. Math. Math. Phys."},{"issue":"3","key":"10.1016\/j.jcp.2026.115061_bib0002","doi-asserted-by":"crossref","first-page":"A1593","DOI":"10.1137\/140979952","article-title":"A singly diagonally implicit two-step peer triple with global error control for stiff ordinary differential equations","volume":"37","author":"Kulikov","year":"2015","journal-title":"SIAM J. on Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115061_bib0003","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.cam.2018.02.037","article-title":"Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods","volume":"340","author":"Kulikov","year":"2018","journal-title":"J. Comput. Appl. Math."},{"issue":"11\u201312","key":"10.1016\/j.jcp.2026.115061_bib0004","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1016\/j.mcm.2005.01.010","article-title":"Construction of explicit Runge\u2013Kutta pairs with stiffness detection","volume":"40","author":"Sofroniou","year":"2004","journal-title":"Math. Comput. Model."},{"issue":"92","key":"10.1016\/j.jcp.2026.115061_bib0005","first-page":"625","article-title":"Symmetric integration rules for hypercubes. III. construction of integration rules using null rules","volume":"19","author":"Lyness","year":"1965","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.jcp.2026.115061_bib0006","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1145\/108556.108575","article-title":"Error estimation in automatic quadrature routines","volume":"17","author":"Berntsen","year":"1991","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"10.1016\/j.jcp.2026.115061_bib0007","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10915-023-02348-6","article-title":"Discontinuity detection by null rules for adaptive surface reconstruction","volume":"97","author":"Bracco","year":"2023","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115061_bib0008","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.cam.2019.05.002","article-title":"Null rules for the detection of lower regularity of functions","volume":"361","author":"Calabr\u00f2","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115061_bib0009","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.cam.2017.05.012","article-title":"Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods","volume":"332","author":"Constantinescu","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115061_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2021.110157","article-title":"A unified framework to generate optimized compact finite difference schemes","volume":"432","author":"Deshpande","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115061_bib0011","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.finel.2019.06.007","article-title":"Variational formulations for explicit Runge\u2013Kutta methods","volume":"165","author":"Mu\u00f1oz-Matute","year":"2019","journal-title":"Finite Elem. Anal. Des."},{"issue":"4","key":"10.1016\/j.jcp.2026.115061_bib0012","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1007\/s42967-021-00159-w","article-title":"Optimized Runge\u2013Kutta methods with automatic step size control for compressible computational fluid dynamics","volume":"4","author":"Ranocha","year":"2022","journal-title":"Commun. Appl. Math. Comput."},{"issue":"2","key":"10.1016\/j.jcp.2026.115061_bib0013","doi-asserted-by":"crossref","first-page":"A612","DOI":"10.1137\/19M1263480","article-title":"Relaxation Runge\u2013Kutta methods: fully discrete explicit entropy-stable schemes for the compressible Euler and Navier\u2013Stokes equations","volume":"42","author":"Ranocha","year":"2020","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115061_bib0014","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.jcp.2019.05.014","article-title":"Paired explicit Runge\u2013Kutta schemes for stiff systems of equations","volume":"393","author":"Vermeire","year":"2019","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115061_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109499","article-title":"Optimal embedded pair Runge\u2013Kutta schemes for pseudo-time stepping","volume":"415","author":"Vermeire","year":"2020","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115061_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.110022","article-title":"Accelerated implicit-explicit Runge\u2013Kutta schemes for locally stiff systems","volume":"429","author":"Vermeire","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115061_bib0017","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.cam.2016.06.013","article-title":"New third-and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations","volume":"316","author":"Weiner","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115061_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109598","article-title":"Highly efficient invariant-conserving explicit Runge\u2013Kutta schemes for nonlinear Hamiltonian differential equations","volume":"418","author":"Zhang","year":"2020","journal-title":"J. Comput. Phys."},{"issue":"4","key":"10.1016\/j.jcp.2026.115061_bib0019","doi-asserted-by":"crossref","first-page":"1398","DOI":"10.1137\/23M1606812","article-title":"Explicit Runge\u2013Kutta methods that alleviate order reduction","volume":"63","author":"Biswas","year":"2025","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2026.115061_bib0020","series-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"Hairer","year":"1993"},{"key":"10.1016\/j.jcp.2026.115061_bib0021","series-title":"Solving Ordinary Differential Equations II","volume":"vol. 375","author":"Wanner","year":"1996"},{"key":"10.1016\/j.jcp.2026.115061_bib0022","series-title":"Numerical Computing with MATLAB","author":"Moler","year":"2004"}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126004146?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126004146?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T13:51:33Z","timestamp":1783086693000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999126004146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":22,"alternative-id":["S0021999126004146"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115061","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the construction of nested explicit Runge\u2013Kutta methods via null rules","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115061","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115061"}}